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Stress, Strain and the Young
modulus
Mark Scheme
Level
A Level
Subject
Physics
Exam Board
Edexcel
Topic
Materials
Sub Topic
Stress, Strain and the Young modulus
Booklet
Mark Scheme
Paper Type
Open-Response 2
Time Allowed:
78 minutes
Score:
/65
Percentage:
/100
Grade Boundaries:
A*
>85%
A
777.5%
B
C
D
E
U
70%
62.5%
57.5%
45%
<45%
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Question
Number
1
Answer
Mark
Explain the difference between elastic deformation and plastic
deformation
QWC – spelling of technical terms must be correct and the answer
must be organised in a logical sequence
Elastic – returns to original shape when deforming force/stress
removed /no permanent deformation
(1)
Plastic – doesn’t return to original shape when deforming
force/stress removed / permanent deformation
(1)
Suitable material or object named which undergoes elastic and
plastic deformation, e.g. spring/wire/strawberry laces – do not
accept rubber / elastic band but accept balloon
(1)
Illustration comparing both types of deformation under
different force / stress / strain / amount of deformation for
material / object (independent of material mark)
(1)
Total for question
Question
Number
2(a)
2(b)
Answer
4
Mark
Explain the meaning of the terms:
Ductile – can be made/drawn into wires /
shows significant/large/lots of plastic deformation / large
plastic region
(1)
Brittle - shatters when subject to impact / sudden force
fails/breaks/cracks with little or no plastic deformation /
breaks just beyond elastic limit / breaks just beyond limit of
proportionality / breaks under stress due to propagation of
cracks
(1)
Calculate the mass that would produce this load.
Use of W = mg
Correct answer (3600 kg)
(1)
(1)
Example of calculation
W = mg
m = 35 000 N / 9.81 N kg-1
= 3570 kg
Total for question
4
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Question
Number
3(a)
Answer
Mark
Explain the meanings of the terms brittle and ductile.
brittle – undergoes no / little plastic deformation (before breaking) /
tends to break when subject to impact [accept breaks just beyond /
soon after limit of proportionality / elastic limit] (1)
graph (1)
ductile – undergoes a lot of plastic deformation (before breaking) / able
to undergo permanent deformation under tensile stress / can be drawn
into wires (1)
graph (1)
[Assume axes labels if not given, accept force, extension labels]
[1 graph mark max if stress strain labels reversed] [Ductile graph can be
curved from start]
3(b)
4
give an example of a ductile material and situation where behaviour
desirable
material example, e.g. copper (accept metal or any metal) (accept
chewing gum, silly putty …) (not rubber)(1)
example of desirable application, e.g. making wires (1)
[NB Not examples of moulding or malleable behaviour]
Total for question
2
6
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Question
Number
4(a)(i)
4(a)(ii)
4(b)
b)
Answer
Stress needed to fracture/break
(do not accept a definition of strong)
Resistance to indentation/scratching
Or resistance to plastic deformation of the surface
Mark
(1)
1
(1)
1
4
(Brass is) strong Or high breaking stress (accept high breaking force)
Or breaking stress is much greater than 10 MPa.
so the key will not break
(Conditional on MP1)
(10MPa/stress) is below the elastic limit
Or the elastic limit is at about 300(± 50) MPa
Or the plastic deformation starts at about 300(± 50) MPa
The key would keep its shape (when the force is removed)
Or the key would not plastically deform
Or any deformation of the key would be elastic
(Conditional on MP3)
(1)
(1)
(1)
(1)
Stiff
Or high Young’s modulus
(1)
The key would not change shape (as it is being used)
(Conditional on MP5)
(1)
(ignore references to tough and limit of proportionality and accept
yield point for elastic limit)
Total for Question
4
6
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Question
Number
5(a)
Answer
Mark
See stress =
Or stress = N m−2
See strain =
5(b)(i)
see σ =
(1)
(1)
.
2
.
Or see E =
∆
(1)
.
see ε =
.
Or substitution into E =
∆
with Δx = 2 (× 10−2 m)
E = (3.5 or 3.6) × 104 Pa
(1)
(1)
3
Example of calculation
σ =
= 10 204 Pa
.
ε=
E=
5(b)(ii)
.
.
= 0.286
.
= 35 678 Pa
The (cross sectional) area would get bigger
(do not allow surface area)
Effect: This would give a smaller value for the Young modulus
Or the value already calculated is too large.
(1)
(1)
2
(If the candidate just states ‘YM will get smaller’ without any
justification, do not award any marks)
(MP2 only for (cross sectional) area gets smaller leading to increase
in Young modulus)
Total for Question
7
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Question
Number
6(a)(i)
*6(a)(ii)
Answer
Mark
Can withstand large stress/ force / tension
Or requires a large stress/force to fracture
1
(QWC – work must be clear and organised in a logical manner using
technical terminology where appropriate)
Max 4 (any two properties and corresponding explanations)
Higher elastic limit
so will return to its original length/shape if greater forces are applied
(if a fly flies into it for the same thickness of silk)
6(b)(i)
(1)
(1)
(1)
Higher ultimate /breaking stress
so stronger Or higher strength Or so the thread could be thinner ( so
less visible to the fly) Or for same (cross-sectional)area can withstand
larger force
(1)
Larger area under the graph
so tougher Or can absorb more energy (and will not break if a fly
stretches the web)
(1)
(1)
(1)
Larger gradient Or steeper Or greater Young modulus Or smaller
strain/extension for the same stress/force
so stiffer
(1)
(1)
Use of the gradient Or correct use of pair of values from linear section
of the graph (up to 0.05 for strain)
(1)
4
Young modulus = 1.5 × 109 Pa
(1)
2
(Accept from 1.45 × 109 Pa to 1.65 × 109 Pa)
Example of calculation
Gradient =
Young Modulus = 1.49 × 109 Pa
6(b)(ii)
Use of E = σ/ Or uses
= 44 (MPa) read from graph
(1)
Use of = 0.03 (or lengths equal to this)
(1)
Use of σ =
(1)
r = 2.0× 10−6 m (ecf from part (b)(i) for YM)
(1)
4
(Accept answers in the range 1.9 × 10−6 m to 2.1 × 10−6 m)
Example of calculation
Stress = 1.49 × 109 Pa × 0.03 = 4.47 × 107 Pa
A=
= 1.30 × 10−11 m2
r=
Total for question
= 2.03× 10−6 m
11
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Question
Number
7(a)(i)
Answer
7(a)(ii)
Mark
Brittle = A
Ductile = B and /or C
Strongest = A
Least stiff = C
(4)
4
A = Glass
B =Steel
C = Copper
(2)
2
3 correct = 2 marks, 1 or 2 correct = 1 mark
One property stated
One behaviour stated
The property and behaviour from the same row in the table and clearly
linked in the candidate’s response
7(b)
Property
High UTS Or strong Or not
brittle
High Young Modulus or stiff
Ductile
Malleable
Elastic
7(c)
8
(1)
3
Behaviour
Will not break when opened/
Will not break when force/stress applied
Grips paper (firmly)
Can be drawn into wires
Can be bent into shape
Will close after being opened
X = yield point
Point at which material shows a large (increase in) strain for a small/no
increase in stress
(Accept the point at which plastic deformation/behaviour/property begins)
Total for Question
Question
Number
(1)
(1)
(1)
(1)
2
11
Answer
•
Markk
Referrence to strain =
(1)
[jjust quoting ∆x/x withoutt defining terrms does nott get the marrk]
•
Comppressive is a decrease in length/squassh/squeeze/causes a negaative
extennsion and tennsile is an inccrease in len
ngth/stretch/pull/causes a (positive)
extennsion
Total for queestion
(1)
2
2
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Question
Number
*9
Answer
Markk
(Q
QWC – Work must be cllear and organised in a lo
ogical manneer using technnical
wording where appropriatte)
Max 5
Malleable for shields
Undergoes (large) plastic deformationn
Under compression Or compressive force Or compressive strress
Question
Number
10*
(1)
(1)
(1)
Ductile for wires
Undergoes large (plastic) deformationn
Under tension Or tensile stress Or tensile force
Total for queestion
(1)
(1)
(1)
Answer
Mark
5
5
(QWC – Work must be clear and organised in a logical manner using
technical wording where appropriate)
Small extension hard to measure accurately (or converse)
(1)
Small extension gives large percentage uncertainty (or converse) (1)
Max 4 from
(thin wire has) small area
(1)
stress = force/area
(1)
so get a larger stress (for a given force) / don’t need such a large force /
need too much force needed if not thin
(1)
greater extension - linked to thinner wire
(1)
strain = extension/original length / extension ˜ original length
greater extension - linked to longer length
(1)
(1)
____________________________________________________________
(Alternative to equation marks:
Young modulus = stress / strain or E = Fx / A∆x (accept alternative
symbols) scores 1 mark, rearranged to make extension the subject scores 2
marks)
Accept converse arguments
(Ignore references to breaking or surface, as in surface area)
Total for question
Max 5
5
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Question
Number
11(a)
11(b)
Answer
(The graph shows) brittle – undergoes no/little plastic
deformation/behaviour (before breaking) /
breaks/fails just beyond/soon after limit of proportionality/elastic limit
(1)
(The graph shows) ductile – undergoes lots of/significant/large plastic
deformation (before breaking) /
able to undergo permanent deformation under tensile stress
(1)
Porcelain/vase/it is brittle
(1)
When broken it doesn’t (permanently) deform/change shape/bend (or
synonyms – but ‘dent’ is not sufficient) (No elastic deformation not
sufficient)
(1)
Total for question
Mark
2
2
4